comyx.fading.rician

comyx.fading.rician#

Module Summary#

Classes#

Rician

Represents the \(\text{Rician}(K, \sigma)\) distribution.

Reference#

class comyx.fading.rician.Rician(K: float, sigma: float = 1)[source]#

Represents the \(\text{Rician}(K, \sigma)\) distribution.

The Rice distribution or Rician distribution (or, less commonly, Ricean distribution) is the probability distribution of the magnitude of a circularly-symmetric bivariate normal random variable, possibly with non-zero mean (noncentral).

Density Function
\[f(x; \nu, \sigma) = \frac{x}{\sigma^2} \exp\left(-\frac{x^2 + \nu^2}{2\sigma^2}\right) I_0\left(\frac{x\nu}{\sigma^2}\right)\]

, where \(I_0\) is the modified Bessel function of the first kind.

Expected value
\[\sigma \sqrt{\frac{\pi}{2}} \exp\left(-\frac{\nu^2}{2\sigma^2}\right)\]
Variance
\[2\sigma^2 + \nu^2 - \frac{\pi\sigma^2}{2}\]
RMS value
\[\sigma \sqrt{2 + \frac{\pi}{2}}\]
Reference:

https://en.wikipedia.org/wiki/Rice_distribution

cdf(x: NDArrayFloat) → NDArrayFloat[source]#

Cumulative distribution function of the the Rician distribution.

Parameters:

x – Value at which cdf is evaluated.

Returns:

Value of the cumulative distribution function evaluated at x.

expected_value() → float[source]#

Returns the expected value of the Rician distribution.

get_samples(size: int | Tuple[int, Ellipsis], seed: int = None) → NDArrayFloat[source]#

Generate random variables from the Rician distribution.

Parameters:

  • size – Nnumber of random variables to generate.

  • seed – Seed for the random number generator.

Returns:

An array of size size containing random variables from the Rician distribution.

pdf(x: NDArrayFloat) → NDArrayFloat[source]#

Probability density function of the Rician distribution.

Parameters:

x – Value at which pdf is evaluated.

Returns:

Value of the probability density function evaluated at x.

rms_value() → float[source]#

Returns the RMS value of the Rician distribution.

variance() → float[source]#

Returns the variance of the Rician distribution.